How do you solve #3^(x^2) + 4x = 1/27#?
This is called a transcendental equation and therefore does not generally have a simple/exact solution. This is because of the x in the exponential and the coefficient. For example,
Generally, the best method of solving these is Newton's method, numerically approximating the solution.
In this case, it is pretty easy for a calculator to find that there is a solution around -1.2 and one around -0.26.